ON TOURNAMENT MATRICES

被引：11

作者：

SHADER, BL ^{[1
]}

机构：

[1] UNIV WISCONSIN,DEPT MATH,MADISON,WI 53706

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1992年 / 162卷

关键词：

D O I：

10.1016/0024-3795(92)90384-M

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let T be a tournament of order n with adjacency matrix M. We find several conditions that are equivalent to M being singular. A correlation between the number of 3-cycles in T and the rank of M is established. It is shown that asymptotically at least 1/2 of the tournament matrices are nonsingular. We also derive bounds on the spectral radius of tournament matrices with a given row-sum vector,

引用

页码：335 / 368

页数：34

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